Algoritmos de integração temporal para solução adaptativa e paralela das equações de Navier-Stokes

Abstract

Turbulent flows are dominant in industrial and everyday applications, due to the inherent advantages of flow characteristics and the difficulty of maintaining flow in the laminar regime. The numerical simulation of turbulent flows presents intrinsic challenges due to the high computational cost for representing the flow structures. In the literature there are several methodologies for an analytical characterization of the contribution of small scales with the objective of achieving a computational cost acceptable to the available resources. One of the most recent methodologies is the variational multi-scale modeling (VMS), which has the advantage of not requiring a filtering of small-scale effects as well as being a generalization of the Petrov-Galerkin stabilization in finite element formulations. The present work seeks to characterize the computational performance of the turbulent flows formulation with VMS modeling for the incompressible Navier-Stokes equations, the first and second order backward difference formulas (BDF) methods are compared, as well as the solution of the linear system using the Jacobian free Newton-Krylov (JFNK) technique and a semi-implicit strategy making use of the BDF discretization. The implementation of the studied reference case was performed using the opensource library libMesh, written in C ++ the library offers several facilities for efficient development of highperformance computing solvers.